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# A = p 4 B = p 5 CP = E[ p 7 , p 2 , p 3 , p 6 , p 1 , p 8 ] S[p 4 , p 5 ] d min = d 45 - PowerPoint PPT Presentation

p 4. p 1. p 6. p 2. p 7. p 8. p 3. p 5. Plane Sweep Algorithm for Closest Pair Problem. A = p 4 B = p 5 CP = E[ p 7 , p 2 , p 3 , p 6 , p 1 , p 8 ] S[p 4 , p 5 ] d min = d 45. E=Event Queue S=Status Queue A,B = Current closest pair CP = Current point

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p4

p1

p6

p2

p7

p8

p3

p5

Plane Sweep Algorithm

for

Closest Pair Problem

A = p4 B = p5 CP =

E[ p7 , p2 , p3 , p6 , p1 , p8 ]

S[p4 , p5 ]

dmin = d45

E=Event Queue S=Status Queue

A,B = Current closest pair

CP = Current point

dmin = Current minimum distance (distance between point A and B)

dij = distance between pi and pj

p4

p1

p6

p2

p7

p8

p3

p5

Previous

A = p4 B = p5 CP =

E[ p7 , p2 , p3 , p6 , p1 , p8 ]

S[ p4 , p5 ]

dmin = d45

d45

New

A = p4 B = p5 CP = p7

E[ p7 , p2 , p3 , p6 , p1 , p8 ]

S[ p4 , p5 , p7 ]

dmin <= min (dmin , d57 ) = d45

p4

p1

p6

p2

p7

p8

p3

p5

Previous

A = p4 B = p5 CP = p7

E[ p2 , p3 , p6 , p1 , p8 ]

S[ p5 , p7 ]

dmin = d45

d45

New

A = p2 B = p7 CP = p2

E[ p2 , p3 , p6 , p1 , p8 ]

S[ p5 , p7 , p2 ]

dmin <= min (dmin , d25 , d27 ) = d27

p4

p1

p6

p2

p7

p8

p3

p5

Previous

A = p2 B = p7 CP = p2

E[ p3 , p6 , p1 , p8 ]

S[ p5 , p7 , p2 ]

dmin = d27

d27

New

A = p2 B = p7 CP = p3

E[ p3 , p6 , p1 , p8 ]

S[ p5 , p7 , p2 , p3 ]

dmin <= d27

p4

p1

p6

p2

p7

p8

p3

p5

Previous

A = p2 B = p7 CP = p3

E[ p6 , p1 , p8 ]

S[p3 ]

dmin <= d27

New

A = p3 B = p6 CP = p6

E[ p6 , p1 , p8 ]

S[ p3 , p6 ]

dmin <= min (dmin , d36 ) = d36

d27

p4

p1

p6

p2

p7

p8

p3

p5

Previous

A = p3 B = p6 CP = p6

E[ p1 , p8 ]

S[p3 , p6 ]

dmin <= d36

New

A = p3 B = p6 CP = p1

E[ p1 , p8 ]

S[ p3 , p6 , p1 ]

dmin <= d36

d36

p4

p1

p6

p2

p7

p8

p3

p5

Previous

A = p3 B = p6 CP = p1

E[ p8 ]

S[ p1 ]

dmin <= d36

New

A = p3 B = p6 CP = p8

E[ p8 ]

S[ p1 , p8 ]

dmin <= d36

d36

Event Queue Is Empty, therefore STOP